CN105785764B - A kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays - Google Patents
A kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays Download PDFInfo
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Abstract
The present invention relates to a kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays, first, flexible vibration is considered as external disturbance, is derived using Lagrangian method and establishes the Spacecraft state-space model containing external disturbance, input delay；Then, it establishes fault model and is integrated into fault model and need in fault-tolerant Spacecraft state model, executing agency's partial failure faults-tolerant control problem is converted by uncertain parameter kinds of robust control problems according to fault model；Finally, Delay-Dependent Liapunov functional and uncertain parameter robust H are utilized∞The method being combined is controlled, the passive fault tolerant control device based on LMI approach design point feedback.This method has the advantages that the simple easy Project Realization of design, suitable for not only there is input delay space industry Spacecraft in the faults-tolerant control of possible actuator partial failure, so that system is kept Asymptotic Stability, and can inhibit to external disturbance.
Description
Technical field
The present invention relates to a kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays, are applied to
The input delay of in-orbit Spacecraft and the posture faults-tolerant control of actuator partial failure.
Background technology
With the continuous development of space technology, the functional diversities of spacecraft, with large-scale flexible appendage (such as the large-scale sun
Can windsurfing etc.) spacecraft it is more and more, flexible vibration is very important for realizing the influence of spacecraft high-precision attitude control.
Simultaneously because the service life of Spacecraft guidance and control is more and more long, the time is also longer in orbit, therefore for the in-orbit fortune of Spacecraft
Higher requirements are also raised for the reliability of control system and safety when row.However, due to spacecraft long-term work vacuum,
In orbit under weightless, temperature change is big and the adverse circumstances of intense radiation and for a long time, it is possible to cause components of system as directed part
Aging causes spacecraft executing agency or sensor to generate failure, and the precision to influence Spacecraft Attitude Control even influences
The stability and reliability of entire control system.Especially actuator, it plays particularly important in spacecraft control
Role, the execution of all control commands is required for the validity of actuator as ensureing.Therefore, when actuator breaks down
When, it may not be possible to the calculated control command of control strategy is fully achieved, therefore control strategy needs there are actuator failures
Certain robustness, that is to say, that realization seems particularly significant for the faults-tolerant control of actuator partial failure failure.In addition, by
Time lag, control of the time lag in Spacecraft can be all generated in the measuring signal transmission of components aging, mechanical wear etc., control system
It is an inevitable problem in system.
In being controlled for the high-precision attitude of Spacecraft, lot of domestic and international scholar is using different methods for scratching
Sufficient research has been done in influence of the vibration of property attachment for spacecraft ontology.But it for existing simultaneously flexible vibration, inputs
The faults-tolerant control of time lag and the Spacecraft of actuator partial failure is not widely studied.
Invention content
The technology of the present invention solves the problems, such as：Time-varying time-delays are inputted when for Spacecraft in orbit and actuator can
The problem of energy partial failure, provides a kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays, nothing
Online fault message is needed, is easily achieved in engineering, and at the same time the sensitivity to input delay is realized, to partial failure failure
Inhibition fault-tolerant and to external disturbance, is mainly used in the posture faults-tolerant control of in-orbit Spacecraft.
Technical solution of the invention is：A kind of more fault-tolerant controls of boundary's dependent robust of Spacecraft of input Time-varying time-delays
Method processed, implementation step are as follows：
The vibration of flexible appendage is considered as external disturbance by the first step, is derived and is established in the presence of input using Lagrangian method
The flexible spacecraft dynamics model of Time-varying time-delays；
Second step models actuator partial failure failure, and fault model is added to the model of first step foundation
In, the system state space model for considering actuator partial failure is established, thus by actuator partial failure faults-tolerant control
Problem is converted into uncertain parameter kinds of robust control problems；
Third walks, and for the system state space model established in second step, utilizes Delay-Dependent Liapunov functional
With uncertain parameter robust H∞The method being combined is controlled, Passive fault-tolerant control feedback control is designed based on LMI approach
Device.
The first step, the interference kinetic model for establishing the Spacecraft system that there are input Time-varying time-delays are realized such as
Under：
Using Lagrangian method derive there are the kinetic models of the Spacecraft of input delay to be：
Wherein t indicates time, θ (t) ∈ Rm×1Indicate attitude angle, J ∈ Rm×mFor the rotary inertia of satellite, η (t) ∈ Rn×1For
The mode of oscillation of flexible appendage, T=diag { 2 ξ1ω1,2ξ2ω2,......2ξnωn}∈Rn×nIndicate modal damping matrix, Λ
=diag { ω1 2,ω2 2,......ωn 2}∈Rn×nIndicate stiffness matrix, ωiFor the vibration frequency of corresponding mode of oscillation, ξi
For the damping of corresponding mode of oscillation, F ∈ Rm×nThe coefficient of coup between spacecraft attitude and flexible structure, FT∈Rn×mFor square
The transposition of battle array F, uF(t- τ (t)) is mounted in the control moment of Spacecraft reaction wheel generation, when wherein τ (t) is time-varying
It is stagnant, and meet τ0＜ τ (t) ＜ τM, τ0And τMThe respectively upper bound of Time-varying time-delays τ (t) and lower bound.
The vibration of flexible appendage is considered as the interference to spacecraft ontology, this model is rewritten as：
Wherein, definition interference
Establish by flexibility be considered as disturbance there are the spacecraft models of input delay.
The second step establishes the system state space model for considering actuator partial failure, actuator part is lost
It is as follows that effect faults-tolerant control problem is converted into the realization of uncertain parameter kinds of robust control problems：
First, the fault model of following actuator partial failure is established,
uF(t- τ (t))=Gu (t- τ (t))
Wherein, G indicates the actuator partial failure factor, and meets following condition：
G=diag { g1,g2,...,gn, gi∈[gxi,gsi],
I=1,2 ..., n, 0≤gxi≤gi≤gsi≤1
Wherein giIt is uncertain constant, gxiAnd gsiIt indicates not knowing constant g respectivelyiLower and upper limit.
It is further simplified model, defines intermediate variable It is as follows with L：
L=diag { l1,l2,...,ln,}
Wherein,
Then have：
| L |=diag | l1|,|l2|,...,|ln|,}
Work as gi=0, it indicates i-th of Actuators Failures, works as gi=1, indicate that i-th of actuator is normal, as 0 ＜ gi＜ 1, table
Show i-th of actuator partial failure.
Then definition status variable and reference output equation are as follows：
It can thus be concluded that the state equation of system is as follows：
Wherein, each coefficient matrix is defined as follows：
C=[Im×m 0m×m]
The Spacecraft system state space model for considering actuator partial failure is established, thus by actuator part
Failure faults-tolerant control problem is converted into uncertain parameter kinds of robust control problems.
The third step, realizes the state feedback controller that the more boundaries of the system state space modelling of foundation rely on
It is as follows：
Design controller u (t- τ (t))=Kx (t- τ (t)) so that closed-loop system：
Asymptotic Stability and meet H∞Performance indicator.I.e.：
(1) as ω (t)=0, above-mentioned closed-loop system is asymptotically stable；
(2) for disturbance input ω (t) the ∈ l of arbitrary non-zero2[0 ,+∞) and given constant γ ＞ 0, in zero initial strip
Under x (t)=0 under part, wherein t ∈ [- h, 0], Hs of the disturbance input ω (t) to controlled output z (t)∞Norm meets：
||z(t)||2≤γ||ω(t)||2
Wherein controller gain K is solved based on LMI approach, i.e., for given scalar γ ＞ 0,
0≤a≤1, τ0,τM,βn＞ 0, n=(1,2,3,4), if there is matrix P ＞ 0, S1＞ 0, Q1＞ 0, Q2＞ 0, Arbitrary Matrix X
With U so that following inequality meets：
Then feedback gain matrix KT=U (XT)-1When, closed-loop system be Asymptotic Stability and under zero initial condition for arbitrary
Disturbance input ω (t) ∈ l2[0 ,+∞) have | | z (t) | |2≤γ||ω(t)||2。
Wherein,
Succinct, the symmetrical matrix in order to writeIn each intermediate variable and symbol definition it is as follows：
M+M is indicated for square formation M, sym (M)T；
Symbol * indicates the corresponding symmetrical item in symmetry square matrix.
The advantages of the present invention over the prior art are that：The posture faults-tolerant control side of the in-orbit Spacecraft of the present invention
Method is Passive fault-tolerant control, does not need online fault message, reduces the difficulty of design.The controller of acquisition can simultaneously be realized to defeated
The sensitivity for entering time lag is easily achieved to the fault-tolerant of partial failure failure and to the inhibition of external disturbance in engineering.
Description of the drawings
Fig. 1 is a kind of design of the more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays of the present invention
Flow chart.
Specific implementation mode
The present invention is described in detail below in conjunction with the accompanying drawings.
There are input delay and the states of executing agency's partial failure when the present invention is directed to Spacecraft in orbit
Spatial model designs a kind of Robust State-Feedback H of new dependence multiple parameters circle∞Fault tolerant control method；First, flexibility is shaken
It is dynamic to be considered as external disturbance, it derives to establish using Lagrangian method and contains external disturbance, the Spacecraft state of input delay
Spatial model；Then, it establishes fault model and is integrated into fault model and need in fault-tolerant Spacecraft state model, root
It converts executing agency's partial failure faults-tolerant control problem to uncertain parameter kinds of robust control problems according to fault model；Finally, sharp
With Delay-Dependent Liapunov functional and uncertain parameter robust H∞The method being combined is controlled, linear matrix inequality is based on
The passive fault tolerant control device of method design point feedback.
As shown in Figure 1, steps are as follows for present invention specific implementation
1, there are the interference kinetic models of the Spacecraft system of input delay for foundation
Using Lagrangian method derive there are the kinetic models of the Spacecraft of input delay to be：
Wherein t indicates time, θ (t) ∈ Rm×1Indicate attitude angle, J ∈ Rm×mFor the rotary inertia of satellite, η (t) ∈ Rn×1For
The mode of oscillation of flexible appendage, T=diag { 2 ξ1ω1,2ξ2ω2,......2ξnωn}∈Rn×nIndicate modal damping matrix, Λ
=diag { ω1 2,ω2 2,......ωn 2}∈Rn×nIndicate stiffness matrix, ωiFor the vibration frequency of corresponding mode of oscillation, ξi
For the damping of corresponding mode of oscillation, F ∈ Rm×nThe coefficient of coup between spacecraft attitude and flexible structure, FT∈Rn×mFor square
The transposition of battle array F, uF(t- τ (t)) is mounted in the control moment of Spacecraft reaction wheel generation, when wherein τ (t) is time-varying
It is stagnant, and meet τ0＜ τ (t) ＜ τM, τ0And τMThe respectively upper bound of Time-varying time-delays τ (t) and lower bound.
The vibration of flexible appendage is considered as the interference to spacecraft ontology, this model is rewritten as：
Wherein, definition interference
Establish by flexibility be considered as disturbance there are the spacecraft models of input delay.
2, the system state space model for considering actuator partial failure is established, by actuator partial failure faults-tolerant control
Problem is converted into uncertain parameter kinds of robust control problems
First, following actuator partial failure fault model is established,
uF(t- τ (t))=Gu (t- τ (t))
Wherein, G indicates the actuator partial failure factor, and meets following condition：
G=diag { g1,g2,...,gn, gi∈[gxi,gsi],
I=1,2 ..., n, 0≤gxi≤gi≤gsi≤1
Wherein giIt is uncertain constant, gxiAnd gsiIt indicates not knowing constant g respectivelyiLower and upper limit.
It is further simplified model, defines intermediate variable It is as follows with L：
L=diag { l1,l2,...,ln,}
Wherein,
Then have,
| L |=diag | l1|,|l2|,...,|ln|,}
Work as gi=0, it indicates i-th of Actuators Failures, works as gi=1, indicate that i-th of actuator is normal, as 0 ＜ gi＜ 1, table
Show i-th of actuator partial failure.
Then definition status variable and reference output equation are as follows：
It can thus be concluded that the state equation of system is as follows：
Wherein, each coefficient matrix is defined as follows：
C=[Im×m 0m×m]
The Spacecraft system state space model for considering actuator partial failure is established, thus by actuator part
Failure faults-tolerant control problem is converted to for uncertain parameter kinds of robust control problems.
3, the state feedback controller relied on for the more boundaries of the system state space modelling of foundation
Design controller u (t- τ (t))=Kx (t- τ (t)) so that closed-loop system：
Asymptotic Stability and meet H∞Performance indicator.I.e.：
(1) as ω (t)=0, above-mentioned closed-loop system is asymptotically stable；
(2) for disturbance input ω (t) the ∈ l of arbitrary non-zero2[0 ,+∞) and given constant γ ＞ 0, in zero initial strip
Under x (t)=0 under part, wherein t ∈ [- h, 0], Hs of the disturbance input ω (t) to controlled output z (t)∞Norm meets：
||z(t)||2≤γ||ω(t)||2
Wherein controller gain K is solved based on LMI approach, i.e., for given scalar γ ＞ 0,
0≤a≤1, τ0,τM,βn＞ 0, n=(1,2,3,4), if there is matrix P ＞ 0, S1＞ 0, Q1＞ 0, Q2＞ 0, Arbitrary Matrix X
With U so that following inequality meets：
Then feedback gain matrix KT=U (XT)-1When, closed-loop system be Asymptotic Stability and under zero initial condition for arbitrary
Disturbance input ω (t) ∈ l2[0 ,+∞) have | | z (t) | |2≤γ||ω(t)||2。
Wherein,
And it is succinct in order to write, it is as follows to define each intermediate variable：
M+M is indicated for square formation M, sym (M)T；
Symbol * indicates the corresponding symmetrical item in symmetry square matrix.
In short, we's invention has the advantages that the simple easy Project Realization of design, suitable for space industry Spacecraft
Not only there is input delay in the faults-tolerant control of possible actuator partial failure, and so that system is kept Asymptotic Stability, and can be right
External disturbance is inhibited.
The content that description in the present invention is not described in detail belongs to the prior art well known to professional and technical personnel in the field.
Claims (4)
1. a kind of more boundary's dependent robust fault tolerant control methods of Spacecraft of input Time-varying time-delays, it is characterised in that including following
Step：
The vibration of flexible appendage is considered as external disturbance by the first step, is derived and is established in the presence of input time-varying using Lagrangian method
The flexible spacecraft dynamics model of time lag；
Second step models actuator partial failure failure, fault model is added in the model of first step foundation,
The system state space model for considering actuator partial failure is established, to turn actuator partial failure faults-tolerant control problem
Turn to uncertain parameter kinds of robust control problems；
Third walks, for the system state space model established in second step, using Delay-Dependent Liapunov functional and not
Determine parameter robust H∞The method being combined is controlled, Passive fault-tolerant control feedback controller is designed based on LMI approach.
2. a kind of Spacecraft more boundary's dependent robusts faults-tolerant control side of input Time-varying time-delays according to claim 1
Method, it is characterised in that：The first step establishes the interference kinetic model for the Spacecraft system that there are input Time-varying time-delays
It realizes as follows：
The kinetic model of Spacecraft that the presence derived using Lagrangian method inputs Time-varying time-delays is：
Wherein t indicates time, θ (t) ∈ Rm×1Indicate attitude angle, J ∈ Rm×mFor the rotary inertia of satellite, η (t) ∈ Rn×1For flexibility
The mode of oscillation of attachment, T=diag { 2 ξ1ω1,2ξ2ω2,......2ξnωn}∈Rn×nExpression modal damping matrix, Λ=
diag{ω1 2,ω2 2,......ωn 2}∈Rn×nIndicate stiffness matrix, ωiFor the vibration frequency of corresponding mode of oscillation, ξiFor
The damping of corresponding mode of oscillation, F ∈ Rm×nThe coefficient of coup between spacecraft attitude and flexible structure, FT∈Rn×mFor matrix
The transposition of F, uF(t- τ (t)) is mounted in the control moment of Spacecraft reaction wheel generation, when wherein τ (t) is time-varying
It is stagnant, and meet τ0＜ τ (t) ＜ τM, τ0And τMThe respectively upper bound of Time-varying time-delays τ (t) and lower bound；
The vibration of flexible appendage is considered as the interference to spacecraft ontology, this model is rewritten as：
Wherein, definition interference
Establish the spacecraft model for the presence input Time-varying time-delays that flexibility is considered as to disturbance.
3. a kind of Spacecraft more boundary's dependent robusts faults-tolerant control side of input Time-varying time-delays according to claim 1
Method, it is characterised in that：The second step establishes the system state space model for considering actuator partial failure, by actuator
Partial failure faults-tolerant control problem is converted into uncertain parameter kinds of robust control problems and is implemented as follows：
First, the fault model of following actuator partial failure is established,
uF(t- τ (t))=Gu (t- τ (t))
Wherein, G indicates the actuator partial failure factor, and meets following condition：
G=diag { g1,g2,...,gn, gi∈[gxi,gsi],
I=1,2 ..., n, 0≤gxi≤gi≤gsi≤1
Wherein giIt is uncertain constant, gxiAnd gsiIt indicates not knowing constant g respectivelyiLower and upper limit；
It is further simplified model, defines intermediate variableIt is as follows with L：
Wherein,
Then have,
Work as gi=0, it indicates i-th of Actuators Failures, works as gi=1, indicate that i-th of actuator is normal, as 0 ＜ gi＜ 1 indicates i-th
A actuator partial failure；
Then definition status variable and reference output equation are as follows：
It can thus be concluded that the state equation of system is as follows：
Wherein, each coefficient matrix is defined as follows：
The Spacecraft system state space model for considering actuator partial failure is established, thus by actuator partial failure
Faults-tolerant control problem is converted into uncertain parameter kinds of robust control problems.
4. a kind of Spacecraft more boundary's dependent robusts faults-tolerant control side of input Time-varying time-delays according to claim 1
Method, it is characterised in that：The third step, depends on the system state space modelling of foundation the state of multiple parameters circle
Feedback controller is implemented as follows：
Design controller u (t- τ (t))=Kx (t- τ (t)) so that closed-loop system：
Asymptotic Stability and meet H∞Performance indicator, i.e.,：
(1) as ω (t)=0, above-mentioned closed-loop system is asymptotically stable；
(2) for disturbance input ω (t) the ∈ l of arbitrary non-zero2[0 ,+∞) and given constant γ ＞ 0, the x under zero initial condition
(t)=0, under wherein t ∈ [- h, 0], Hs of the disturbance input ω (t) to controlled output z (t)∞Norm meets：
||z(t)||2≤γ||ω(t)||2
Wherein controller gain K is solved based on LMI approach, i.e., for given scalar γ ＞ 0,0≤a
≤ 1, τ0,τM,βn＞ 0, n=1,2,3,4, if there is matrix P ＞ 0, S1＞ 0, Q1＞ 0, Q2＞ 0, Arbitrary Matrix X and U make
Following inequality meets：
Then feedback gain matrix KT=U (XT)-1When, closed-loop system be Asymptotic Stability and under zero initial condition for Arbitrary Perturbation
Input ω (t) ∈ l2[0 ,+∞) have | | z (t) | |2≤γ||ω(t)||2,
Wherein,
Symmetrical matrixIn each intermediate variable and symbol definition it is as follows：
M+M is indicated for square formation M, sym (M)T；Symbol * indicates the corresponding symmetrical item in symmetry square matrix.
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| CN108133066A (en) * | 2016-11-30 | 2018-06-08 | 中国科学院沈阳自动化研究所 | A kind of design method of satellite output feedback fault-tolerant controller |
| CN108121202A (en) * | 2016-11-30 | 2018-06-05 | 中国科学院沈阳自动化研究所 | A kind of feedback of status switch controller design method based on delayed switching strategy |
| CN109507878A (en) * | 2017-09-15 | 2019-03-22 | 中国科学院沈阳自动化研究所 | State based on average residence time switching feeds back switch controller design method |
| CN108572552B (en) * | 2018-04-24 | 2021-04-27 | 杭州电子科技大学 | Mixed passive/H based on fault alarm∞In a hybrid control method |
| CN108927803A (en) * | 2018-07-25 | 2018-12-04 | 西北工业大学 | One kind arresting antihunt means in continuous impact conditions down space robot target |
| CN110011585B (en) * | 2019-05-20 | 2020-11-24 | 中国矿业大学 | Permanent magnet semi-direct drive type transmission shafting torsional vibration control method caused by external excitation |
| CN110361973B (en) * | 2019-07-15 | 2022-10-14 | 南京信息工程大学 | Fault-tolerant control method of time-lag singular perturbation system |
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